Barcelona Toward an error model for radar quantitative precipitation estimation in the Cévennes- Vivarais region, France Pierre-Emmanuel Kirstetter, Guy Delrieu, Brice Boudevillain, Alexis Berne Laboratoire d’étude des Transferts en Hydrologie et Environnement, Grenoble, France ERAD2006, Barcelona

Scope target: characterize the residual QPE error by mean of probability distributions and space-time structure Reference rainfall : Rref(A,t) (raingauge, geostatistics) Radar estimated rainfall : R*(A,t) = f(radar calibration, ground interactions, vertical structure of atmosphere, Z-R relationship, …) see B. Boudevillain O3.12 ERAD2006-A-0021 Residual error : ε(A,t) = R*(A,t) - Rref(A,t) radar raingauge 8-9 sept oct nov nov dec 2002 max 700 mm max 80 mm max 150 mmmax 300 mm

Outline Reference rainfall Error model: statistic distributions of residuals Error model: space-time structure Conclusions and perspectives target: characterize the residual QPE error by mean of probability distributions and space-time structure ε values ε

Reference rainfall : kriging raingauge values Kriging: an interpolation estimator  linear: interpolated value (t 0 ) = L.C. (measured values t i )  unbiased: E(interpolated value) = E(real value)  optimum: minimizes the estimation variance t1t1 t2t2 t3t3 t4t4 t0t0 The variogram function characterizes the rainfall structure (Journel and al., 1978)  The nugget  The range  The sill

Reference rainfall at even time step: mapping kriged raingauge accumulation data map estimation standard deviation map variogram range=50 nugget=0

Reference rainfall at hourly time step: mapping kriged raingauge accumulation data map We consider geographical domains with low estimation variance : 1-km² resolution containing a raingauge estimation standard deviation map range=33 nugget=0 variogram

Symetric distributions for ε (Gaussian, centered exponential models) Evolution to be conditioned by: - radar rainfall rate estimates - distance from radar - time step Conditional distributions of the residuals « reference - radar » (1-km²space step ; hourly time step) centered exponential model empirical distribution Residuals ε « Rref – R* » (mm/h) R* radar estimates (mm/h) raingauges (mm) radar (mm)

Conditional distributions of the residuals « radar - reference » ε evolution with rainfall rate, distance from radar and time step (1-km²space step) distances from radar < 60kmdistances from radar > 60km mean « Rref – R* » (mm/h) standard deviation (mm/h) radar rainfall rate (mm/h) hours hour

Error model: space structure of the residuals (hourly time step) Distance from radar < 60 kmDistance from radar > 60 km range=30 nugget=0 range=55 nugget=0.1

Error model: temporal structure of the residuals ε (hourly time step) range=1.8 h nugget=4 sill = 10.5range=1.8 h nugget = 6 sill = 10.9 Distance from radar < 60 kmDistance from radar > 60 km temporal difference (hours)

Conclusions Perspectives: bias and residual structures show radar data processing can be improved. study dependence of residuals with rainfall type. conditional simulation to assess impact of rainfall uncertainties upon hydrological simulation. Results: residual distributions are fairly symetric and well fitted by exponential models. Mean and standard deviation depend on rainfall rate estimates and distance from radar. residuals are significatively (unfortunately) spatially and temporally correlated. To keep in mind: radar rainfall estimates have a complex error structure. raingauge estimates are not an absolute reference but geostatistics provide powerful tools to assess the reference quality. the error model is empirical and depends on climatological context and radar data processing.

Thanks for your attention

Realisations in terms of observation (1/4) CV operational data: collection, critical analyse and creation of a database 3 weather radar systems (2 S-band, 1 C-band), 200 hourly rain gauges (1/65 km2), 500 daily raingauges (1/25 km2),40-50 discharge stations, 6 hydromet services… To appear soon: rain re-analyses and rainfall-runoff balances (10 – 2500 km²)

3.La chasse aux canards Colognac SommièresAnduze Colognac Sommières Anduze

3.La chasse aux canards Colognac SommièresAnduze Bourg St Andéol

24 novembre 2002 Reference rainfall

Idea :  error model  design possible rainfall fields  conditional simulation to assess impact of rainfall uncertainties upon hydrological simulation Estimated rainfall radar (mm/h) Reference rainfall raingauge (mm/h) catchment

Aim : quantify potential error for radar systems operating in mountainous regions (Pellarin et al., 2002) A first approach : the « hydrologic visibility » Radar parameters : beamwith, wavelenght… Radar waves-ground interactions Arc méditerranéen ; ALICIME, 2004 Vertical structure of the atmosphere

Main rainfall events during autumn Sept Oct Nov Nov Déc Rainfall field : kriged raingauges data Rainfall field : radar